Problem: N different natural numbers are given. If you select four different ones and set them as $ A $, $ B $, $ C $, $ D $, the following formula

$ \ Frac {A + B} {C --D} $



I want to find the maximum value of.




Given N different natural numbers, choose 4 different from them and create a program to find the maximum value of the above formula.



Input

The input is given in the following format.


N
a1 a2 ... aN


The number N (4 ≤ N ≤ 1000) of natural numbers is given in the first line. The value ai (1 ≤ ai ≤ 108) of each natural number is given in the second line. However, the same natural number does not appear more than once (ai ≠ aj for i ≠ j).

Output

Outputs the maximum value of the above formula as a real number for a given N natural numbers. However, the error must not exceed plus or minus 10-5.

Examples

Input

10
1 2 3 4 5 6 7 8 9 10


Output

19.00000


Input

5
22 100 42 3 86


Output

9.78947


Input

6
15 21 36 10 34 5


Output

18.00000


Input

4
100000 99999 8 1


Output

28571.285714

Solution (in CPP):

Solution:
#include<bits/stdc++.h>
using namespace std;
#define MOD 1000000007
#define INF 1000000010
#define EPS 1e-9
#define fst first
#define scd second

#define debug(x) cout<<x<<endl;
#define repi(i,x,n) for(int i=x;i<n;i++)
#define rep(i,n) repi(i,0,n)
#define lp(i,n) repi(i,0,n)
#define repn(i,n) for(int i=n;i>=0;i--)
#define int long long
#define endl "\n"


signed main(){
  cin.tie(0);	
  ios::sync_with_stdio(false);
  cout<<fixed<<setprecision(12);
  int n;
  cin>>n;
  int a[1000];
  rep(i,n) cin>>a[i];
  sort(a,a+n);
  double ans=0;
  rep(i,n-2){
    ans=max((double)(a[n-1]+a[n-2])/(double)(a[i+1]-a[i]),ans);
  }
  ans=max((double)(a[n-3]+a[n-4])/(double)(a[n-1]-a[n-2]),ans);
  ans=max((double)(a[n-1]+a[n-4])/(double)(a[n-2]-a[n-3]),ans);
  cout<<ans<<endl;

  return 0;
}